The formation of partial dislocations in Ge/Si(001) structures is theoretically investigated by the atomistic model. The equilibrium critical thickness of nucleation for 90° partial with an extrinsic stacking fault is about half of that for 60° perfect dislocations in the shuffle-set configuration. A 60° dislocation is predicted to be (i) in the narrowly dissociated glide-set configuration with an intrinsic stacking fault when interaction with another dislocation is absent, (ii) in the dissociated glide-set configuration with an extrinsic stacking fault when there is another 60° dislocation with parallel screw component in the vicinity, and (iii) in the undissociated configuration or in the narrowly dissociated configuration with an intrinsic fault when there is another 60° dislocation with opposite screw component in the vicinity. In the dissociated configurations, the 90° partial remains at the interface, and the 30° partial is displaced into the Ge layer in the extrinsic fault dissociation and into the substrate in the intrinsic fault dissociation.